Scale-free Phenomena Research Articles

Time-resolved correlation of distributed brain activity tracks E-I balance and accounts for diverse scale-free phenomena

Much of systems neuroscience posits the functional importance of brain activity patterns that lack natural scales of sizes, durations, or frequencies. The field has developed prominent, and sometimes competing, explanations for the nature of this scale-free activity. Here, we reconcile these explanations across species and modalities. First, we link estimates of excitation-inhibition (E-I) balance with time-resolved correlation of distributed brain activity. Second, we develop an unbiased method for sampling time series constrained by this time-resolved correlation. Third, we use this method to show that estimates of E-I balance account for diverse scale-free phenomena without need to attribute additional function or importance to these phenomena. Collectively, our results simplify existing explanations of scale-free brain activity and provide stringent tests on future theories that seek to transcend these explanations.

Eigenvalue-based entropy and spectrum of bipartite digraph

Graph entropy is an important measure of the evolution and complexity of networks. Bipartite graph is a special network and an important mathematical model for system resource allocation and management. In reality, a network system usually has obvious directionality. The direction of the network, or the movement trend of the network, can be described with spectrum index. However, little research has been done on the eigenvalue-based entropy of directed bipartite network. In this study, based on the adjacency matrix, the in-degree Laplacian matrix and the in-degree signless Laplacian matrix of directed bipartite graph, we defined the eigenvalue-based entropy for the directed bipartite network. Using the eigenvalue-based entropy, we described the evolution law of the directed bipartite network structure. Aiming at the direction and bipartite feature of the directed bipartite network, we improved the generation algorithm of the undirected network. We then constructed the directed bipartite nearest-neighbor coupling network, directed bipartite small-world network, directed bipartite scale-free network, and directed bipartite random network. In the proposed model, spectrum of those directed bipartite network is used to describe the directionality and bipartite property. Moreover, eigenvalue-based entropy is empirically studied on a real-world directed movie recommendation network, in which the law of eigenvalue-base entropy is observed. That is, if eigenvalue-based entropy value of the recommendation system is large, the evolution of movie recommendation network becomes orderless. While if eigenvalue-based entropy value is small, the structural evolution of the movie recommendation network tends to be regular. The simulation experiment shows that eigenvalue-based entropy value in the real directed bipartite network is between the values of a directed bipartite small world and a scale-free network. It shows that the real directed bipartite network has the structural property of the two typical directed bipartite networks. The coexistence of the small-world phenomena and the scale-free phenomena in the real network is consistent with the evolution law of typical network models. The experimental results show that the validity and rationality of the definition of eigenvalue-based entropy, which serves as a tool in the analysis of directed bipartite networks.

Prozesu estokastikoak fisikan eta ekonomian: higidura browndarretik finantza-merkatuen ereduetara

Azken hamarkadetan, ikerkuntza-talde anitzek, fisikan garatutako metodoak erabili dituzte merkatuen portaera aztertzeko. Izan ere, merkatuetako ezaugarri estatistiko sinple batzuen unibertsaltasuna nabarmena da: eskala-menpekotasunik gabeko fenomenoak antzeman daitezke (itzulkinen probabilitate-banaketetan, adibidez), fisikako hainbat esparrutan agertzen diren gisan. Hala, fisikarientzat, ekonomia ikertzea, ongi definitutako sistema konplexu bati buruzko datu ugari aztertzea bilakatu da. Aztertze-metodologia garrantzitsuenetariko bat, adibidez, prozesu estokastikoak erabiltzean datza. Izan ere, fisikan, ezaugarri unibertsalak dituzten sistema konplexu batzuen kasuan, eredu deterministak ez dira baliagarriak. Bi esparruen arteko paralelismotik, hortaz, ikuspegi estokastikoa ekonomiaren esparruan sartzea, eta merkatu estokastiko bat ereduztatzea zilegi litzateke. Hau da, kontzeptu matematiko beraz baliatuz, posible da eredu fisiko eta ekonomiko bat independenteki sortzea.

Fuzzy ARTMAP driven features selection: towards a system to design information fusion for the geographic discovery

The availability of ground-level and overhead images is increasing fast. However, the potentialities of joint usage of these images on information fusion systems for in-deep geographic discovery, by answering the typical binomial quest: what and where are still to be completely evaluated. It is, therefore, necessary to establish a variety of procedures to study these potentialities including on how to assess domain-invariance between this imagery related to ground-level and overhead capture domains for example. We addressed in this paper a novel framework for one prospect for an optimal set of handcrafted domain-invariant features for ground the optimized usage of multiple sources of information on a feature level based fusion system. All of this was done framed by the usage of small datasets and, also, of interpretable classifiers (human-centered computing) and it paves the way towards the proposition of application software to be used potentially as a didactic tool with emphasis on the botanic domain. The results also endorse a domain-invariance that was already implicit on the results of previously published papers. Broadly evaluating, these results connecting image datasets on contrasting scales can launch new investigations in the scope of scale-free phenomena.

Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy

The spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to characterize scale-free phenomena and reflect the local features of random multi-scaling structure. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on different entropy concepts. Three representative fractal dimensions in the multifractal dimension set, capacity dimension, information dimension, and correlation dimension, are utilized to make empirical analyses of the urban form of two Chinese cities, Beijing and Hangzhou. The results show that the entropy values vary with the measurement scale, but the fractal dimension value is stable is method and study area are fixed; if the linear size of boxes is small enough (e.g., <1/25), the linear correlation between entropy and fractal dimension is significant (based on the confidence level of 99%). Further empirical analysis indicates that fractal dimension is close to the characteristic values of spatial entropy. This suggests that the physical meaning of fractal dimension can be interpreted by the ideas from entropy and scaling and the conclusion is revealing for future spatial analysis of cities.

Scale-free brain ensemble modulated by phase synchronization

To listen to brain activity as a piece of music, we proposed the scale-free brainwave music (SFBM) technology, which could translate the scalp electroencephalogram (EEG) into music notes according to the power law of both EEG and music. In the current study, this methodology was further extended to a musical ensemble of two channels. First, EEG data from two selected channels are translated into musical instrument digital interface (MIDI) sequences, where the EEG parameters modulate the pitch, duration, and volume of each musical note. The phase synchronization index of the two channels is computed by a Hilbert transform. Then the two MIDI sequences are integrated into a chorus according to the phase synchronization index. The EEG with a high synchronization index is represented by more consonant musical intervals, while the low index is expressed by inconsonant musical intervals. The brain ensemble derived from real EEG segments illustrates differences in harmony and pitch distribution during the eyes-closed and eyes-open states. Furthermore, the scale-free phenomena exist in the brainwave ensemble. Therefore, the scale-free brain ensemble modulated by phase synchronization is a new attempt to express the EEG through an auditory and musical way, and it can be used for EEG monitoring and bio-feedback.

Small-world or Scale-Free Phenomena in Internet: What Implications for the Next-generation Networks?

AbstractThe paper examines the large-scale topological structure of the Internet in order to see whether the structure exhibits some features that lead Internet Services Providers to go aside further collaboration for the deployment of next-generation networks. The results indicate the existence of positive signs or early stages of possible move towards more cooperative relationships, mainly among backbones. These findings have implications for the next-generation networks policy and strategy, particularly the move towards strategic alliances after the recent phase of mergers and acquisitions.Keywords: Next-generation networks, Internet, Alliances, Small-world, Scale-free, Internet services providers1. IntroductionThe debate in the literature about the next-generation networks rotates around two major issues relating to the evolution of economic business models and of regulations (see for example (Frieden, 2003, 2007). Whether the debate on regulation seems of most concern in the United States, while European institutions and Japanese government are just beginning to focus on (Cave et al., 2009; Wallsten and Hausladen, 2009, Cave 2010; Ruhle and Lundborg, 2010), it is important to consider the impact of any changes on the future of the industry. Further, the debate emphasizes two opposite views, which could be dealing with the 'Net Neutrality' controversy or neutrality restrictions. On the one side, some are against Net neutrality. They argue that Net neutrality rules would reduce incentives to upgrade networks and launch next generation network services. They underline that in the absence of Net neutrality pricing would be more flexible and Quality of Service (QoS) better achieved (Felten, 2006; Lessig, 2006; Hahn and Wallsten, 2006; Clarke, 2009). This argument is supported by Internet broadband providers ATT Caves et al., 2009). They believe that broadband providers will use their market power to block the applications they do not favour and will also discriminate between contents providers (i.e. websites, services, protocols). This argument is supported by large web content companies such as Google, Yahoo or MSN.Going along these debates, several questions could be raised. Who should bear the cost of the new-generation infrastructure? How can Quality of Service be achieved efficiently? How can cooperation and trust be strengthened between operators?To answer these questions we need firstly to start to study the topological structure of ISPs' relationships. In other words, to see whether the current structure of interconnection network between ISPs exhibit some features that enable to go for further collaboration, and at which level of the structure this is more likely to occur. Though some studies have examined the topological structure of Internet (Amaral et al., 2000; Barabasi, 2002; Vasquez et al.,2002; Yan and Assimakopoulos, 2009), to the best of my knowledge, none has addressed the strategic implications.We argue our approach or method by two points. First, ISPs are already bound by a preliminary agreement of collaboration through peering agreements. Indeed, to achieve universal connectivity and exchange traffic Internet providers have to settle interconnection agreements. Interconnection agreements are of two sorts: peering and transit. Whether transit agreement involves a fees payment by customer to provider, a peering agreement is a bilateral peer-to-peer relationship where Internet providers do not charge each other for terminating traffic. It involves the exchange traffic for free between them. Therefore, the peering agreement could be considered as a preliminary agreement of collaboration between two Internet providers. Second, some recent studies have shown that asymmetric effect was one major factor that has a negative and significant impact on tying a peering agreement (Carter and Wright, 2003; Weiss and Shin, 2004; Badasyan and Chakrabarti, 2008; Shrimali and Kumar, 2008; Jahn and Prufer, 2008; Lippert and Spagnalo, 2008). …

Connectivity and Competition in Airline Networks: A Complexity Analysis of Lufthansa's Network

Information, communication and transport networks have always been in a state of flux, while they also influence each other. Extensive research efforts have been made to investigate the dynamics in the structure and use of networks, e.g., by means of network geometries, small-world effects and scale-free phenomena. We will illustrate these new developments on the basis of airline network evolution. The present paper provides a new contribution to the analysis of topological properties of complex airline networks. Using Lufthansa's networks as an example, this paper aims to show the empirical relevance of various network indicators - such as connectivity and concentration - for understanding changing patterns in airline network configurations. After an extensive discussion of various statistical results, a decision-aid method, viz. multi-criteria analysis, is used to investigate the robustness of our findings. The results highlight the actual strategic choices made by Lufthansa for its own network, as well in combination with its partners in Star Alliance.

Research on video similarity network

In order to solve the problem that is close to the scale-free phenomena in the complex network theory when the video appears in the virtual information system,a brand-new network of video semantic similarity was designed.The description model of video semantics,the construction rule of the network,the computation method and retrieval algorithm based on the network were given in detail.Experiments have been made on this video similarity network.The results show that it can effectively solve the problem caused by the usage of videos.

Principles and methods for the validation of quantitative remote sensing products

We first discuss the relativity of “true value and homogeneity” for quantitative remote sensing products (QRSPs), and then propose the definitions of “eigenaccuracy” and “eigenhomogeneity” under practical conditions. The eigenaccuracy and eigenhomogeneity for land surface crucial parameters such as albedo, leaf area index (LAI), and surface temperature are analyzed based on a series of experiments. Secondly, we point out the differences and similarities between the scale-free phenomena of the QRSPs and the measurements of the coastline length (1-dimensional) and the curved surface area (2-dimensional). An information fractal algorithm for the QRSPs is presented. In a case study for the LAI, when the fractal dimension is 2.16, the ratio of the LAI retrieval values obtained respectively from remote sensing data of 30 m and 6 km pixel resolution can actually reach as high as 2.86 for the same 6 km pixel using the same retrieval model. Finally, we propose an operational validation method “one test and two matches” and multipoint observation when the real situation does not allow carrying out scanning measurement without gap and overlap on the ground surface.

Power Laws in Elections - A Survey

Empirical power laws in general elections are surveyed in Brazil, Mexico, India, and with focal analysis in Indonesia. The diversity of preference dynamics in voter’s social network and the way multi-party systems to be in its critical conditions are responsible for this pushing around the evolution of political system at general. For the special case of Indonesia, we report the existing robustness for levels of legislative elections throughout 1999 to 2009. We show that the scale free phenomena in different scales of aggregation and outline some analytical outlines and consequences that could be drawn referring to this.

Influence of user requirement behaviors on internet collective dynamics

The complex network dynamics of the Internet is mainly influenced by user requirement behaviors, and can be statistic in time series. A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions and small-world phenomena. This paper analyzed the empirical collective behavior of user requirements in a region, and discovered that the frequency and the in-degree distributions of bipartite networks constructed by user visiting web sites follows the power-law, and the exponent is between 1.7 and 1.8. A novel two-tier model, the virtual resource networks (VRN) and physics topology networks (PTN), is proposed to study the influences on the Internet collective behaviors. The mapping process mechanisens of VRN to PTN simulates how the dynamic behaviors of resource network influence the internet physics topology networks. The power-law characteristics of VRN can bring forth the result that the phase transition critical point moves left and network performance is more incapable. The distributed mapping process of VRN to PTN was constructed for the small subset with the high degree nodes, then the phase transition critical point of PTN moves right and the network performance is improved obviously.

Evolving model of weighted networks inspired by scientific collaboration networks

Inspired by scientific collaboration networks (SCN), especially our empirical analysis of econophysicists network, an evolutionary model for weighted networks is proposed. Besides a new vertex added in at every time step, old vertices can also attempt to build up new links, or to reconnect the existing links. The number of connections repeated between two nodes is converted into the weight of the link. This provides a natural way for the evolution of link weight. The path-dependent preferential attachment mechanism with local information is also introduced. It increases the clustering coefficient of the network significantly. The model shows the scale-free phenomena in degree and vertex weight distribution. It also gives well qualitatively consistent behavior with the empirical results.

Econophysics: can physicists contribute to the science of economics?

How can computational physicists contribute to the search for solutions to the puzzles posed by modern economics that economists themselves cannot solve? An approach-not very commonly used in economics-is to begin empirically, with real data that you can analyze in some detail, but without prior models. In economics, a great deal of real data is available. If you, moreover, have at your disposal the tools of computational physics and the computing power to carry out any number of approaches, this abundance of data is a great advantage. A careful analysis of any system involves studying the propagation of correlations from one unit of the system to the next. We learned that these correlations propagate both directly and indirectly. At one time, it was imagined that scale-free phenomena are relevant to only a fairly narrow slice of physical phenomena. However, the range of systems that apparently display power-law and hence scale-invariant correlations has increased dramatically in recent years. Such systems range from base-pair correlations in noncoding DNA, lung inflation, and interbeat intervals of the human heart, to complex systems involving large numbers of interacting subunits that display free will. In particular, economic time series, e.g., stock market indices or currency exchange rates, depend on the evolution of a large number of strongly interacting systems far from equilibrium, and belong to the class of complex evolving systems. Thus, the statistical properties of economic time series have attracted the interests of many physicists.

Fractal landscapes in biological systems: Long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having in common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis. whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.